Triangulation is a traditional and popular method of attaining the coordinates of an object by the use of usually two or more sensors. Sensors used for triangulation need only give a bearing to the object, the distance being the unknown variable. The sensors can either be active, i.e. irradiate the object with for example electromagnetic radio waves that reflect off the object for detection, or more usually be passive, i.e. the sensors rely on being able to detect a bearing to an object by emissions of the object such as radio waves emitted by a mobile telephone. The traditional use of triangulation has been to locate illegal radio transmitters for pirate radio stations. Currently triangulation can be used in an even greater variety of applications, such as finding lost people by means of a turned-on mobile telephone.
The commonly at least two sensors used, each give a bearing/measurement to the object in question. The given bearing from each sensor is related to the location and most importantly the orientation of each respective sensor, i.e. bearings from a sensor are related to the spatial location and orientation of the sensor. Usually the sensor is at the origin of a polar coordinate system, where a bearing is related to some coordinate axis. Each sensor thus has its own coordinate system, or rather its own reference system. To easily be able to use the bearings from more than one sensor it is desirable that the sensors are related to a single reference system. Unfortunately the surface of the earth has a definite curvature, making the likelihood very small that the reference systems of two sensors that are widely spaced will coincide. It is most likely that the reference systems of two different sensors are both revolved and rotated in relation to each other.
If the sensors are close to each other, in the range of a few kilometers, then the curvature of the earth is commonly ignored and the reference systems of the different sensors are considered to coincide. The resulting errors are usually relatively small in relation to other error sources. On the other hand, if the sensors are further apart, it is no longer possible to ignore the problems that are incurred by different reference systems. Methods to take this into account usually involve approximating the curved surface by geometrical algorithms such that it can be considered flat by the introduction of a map system. Map systems will usually also take into account any meridional convergence by means of the algorithms. Unfortunately the use of a map system will introduce errors in dependence on how good the different approximations are. For example, densely populated areas will usually have very good map systems, because a lot of effort has been put into them, while on the other hand thinly populated areas, where it is likely for people to get lost, might have very poor approximations of the earth's curvature, if the area is covered by the map system at all. There still exists room for improvement of triangulation systems.